8. Among 38-43 year old, 25% say they have written an editorial letter while under the influence of peer pressure. Suppose two 38-43 year old are selected at random. (a )what is the probability that at least one has not written under the influence of peer pressure. (b) what is the probability of that at least one has written an editorial letter while under the influence of peer pressure.
To answer these questions, we will use the concept of probability. Probability is a measure of the likelihood of an event occurring. It is calculated by dividing the number of favorable outcomes by the total possible outcomes.
Given information:
- Among 38-43 year olds, 25% say they have written an editorial letter under the influence of peer pressure.
- Two 38-43 year olds are selected at random.
Let's calculate the probabilities step by step:
(a) What is the probability that at least one has not written under the influence of peer pressure?
To find this probability, we need to calculate the probability that both individuals have written under the influence of peer pressure and subtract it from 1.
Probability that both have written under the influence of peer pressure:
P(Both written) = P(1st written) * P(2nd written) = 0.25 * 0.25 = 0.0625
Now, subtracting it from 1 will give us the probability that at least one has not written under the influence of peer pressure:
P(At least one not written) = 1 - P(Both written) = 1 - 0.0625 = 0.9375
Therefore, the probability that at least one 38-43 year old has not written an editorial letter under the influence of peer pressure is 0.9375 or 93.75%.
(b) What is the probability that at least one has written an editorial letter under the influence of peer pressure?
To find this probability, we will use the same approach. The only difference is that we want to find the probability that at least one person has written under the influence of peer pressure, rather than not written.
Probability that at least one has written under the influence of peer pressure:
P(At least one written) = 1 - P(Both not written) = 1 - (P(1st not written) * P(2nd not written))
P(At least one written) = 1 - (0.75 * 0.75) = 1 - 0.5625 = 0.4375
Therefore, the probability that at least one 38-43 year old has written an editorial letter under the influence of peer pressure is 0.4375 or 43.75%.
To answer these questions, we can use probability calculations.
(a) To find the probability that at least one person has not written under the influence of peer pressure, we need to determine the probability that both individuals have written under the influence of peer pressure and subtract it from 1.
The probability that a randomly selected 38-43-year-old individual writes an editorial letter under the influence of peer pressure is 25% or 0.25. Therefore, the probability that both individuals have written under the influence of peer pressure is:
P(both have written under peer pressure) = P(person 1 has written under peer pressure) × P(person 2 has written under peer pressure)
P(both have written under peer pressure) = 0.25 × 0.25 = 0.0625
So, the probability that at least one person has not written under the influence of peer pressure is:
P(at least one has not written under peer pressure) = 1 - P(both have written under peer pressure)
P(at least one has not written under peer pressure) = 1 - 0.0625
P(at least one has not written under peer pressure) = 0.9375 or 93.75%
(b) To find the probability that at least one person has written an editorial letter under the influence of peer pressure, we also need to determine the complementary event to having at least one person not writing under peer pressure.
P(at least one has written under peer pressure) = 1 - P(at least one has not written under peer pressure)
P(at least one has written under peer pressure) = 1 - 0.9375
P(at least one has written under peer pressure) = 0.0625 or 6.25%